Solving Trig Functions

Question

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)

sin 𝜃 =

-squareroot(3)/2

List six specific solutions.

Answer 1

sinT = -sqr3/2

T= sin^-1(-sqr3/2)

reference angle = 60 degrees or pi/3

Theta is in quadrant III or IV where sines are always negative

T = 240, 330, 600, 690, 960, 1050 degtees

or

T =4pi/3, 5pi/3, 10pi/3, 11pi/3, 16pi/3, 17pi/3 radians

T = 240+36k or 330+360k where k= any integer

or

T = 4pi/3 +2kpi or 5pi/3+2kpi where k= any integer

there is an infinite number of solutions for Theta